Kapteyn's (m, log r) Table and Cosmology

Abstract

The (m, log r) table is a useful tool in solving the fundamental equation of stellar statistics. We discuss Kapteyn's use of the table in 1902 in studying the distribution of stars. Recently, the table has been adapted to serve in cosmological studies, where the role of distance is taken over by the redshift. We address the bin size used in the table and show that it might as well be made vanishly small, leading to the concepts of V_(max) and V/V_(max) for individual objects of an observed sample. We discuss some applications of the V/V_(max) test for quasars and for gamma-ray bursts.

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